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Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory

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Abstract

In this paper the nonlinear wave equation

$$u_u - u_{xx} + v(x)u(x,t) + \varepsilon u^3 (x,t) = 0$$

is studied. It is shown that for a large class of potentials,v(x), one can use KAM methods to construct periodic and quasi-periodic solutions (in time) for this equation.

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Authors and Affiliations

  1. Department of Mathematics, The Pennsylvania State University, 16802, University Park, PA, USA

    C. Eugene Wayne

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  1. C. Eugene Wayne
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Communicated by A. Jaffe

Supported in part by NSF grants DMS-86-02001 and DMS-88-02118

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Wayne, C.E. Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory. Commun.Math. Phys. 127, 479–528 (1990). https://doi.org/10.1007/BF02104499

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  • DOI: https://doi.org/10.1007/BF02104499

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